Gamma in GR

Does the Lorentz factor show up much (or at all) in general relativity? For instance, is it appropriate to use it as part of the four-momentum vector when finding the components of the stress-energy tensor even in a non-flat spacetime? I was wondering because the derivations of it that I've seen always assume either a Euclidean or Minkowskian metric.

From what I understand, gamma does play a direct role in general relativity.

Both gravitational and kinematic time dilation contribute toward the relativistic precession of an orbiting mass (ex: Mercury around the Sun), where kinematic time dilation is what arises from special relativity.

In terms of "orbits per orbit" of relativistic precession, where r is the average orbit radius (semi-major axis), a common formula is:

[tex]\delta = \frac{3GM}{rc^2}[/tex]

Two-thirds of this is from gravitational time dilation (due to the gravitational field of the source mass), and one-third from kinematic time dilation (due to the current velocity of the orbiting mass in relation to the source mass).

The value [tex]\delta 2\pi[/tex] gives the relativistic precession in terms of radians per orbit.

Does the Lorentz factor show up much (or at all) in general relativity? For instance, is it appropriate to use it as part of the four-momentum vector when finding the components of the stress-energy tensor even in a non-flat spacetime? I was wondering because the derivations of it that I've seen always assume either a Euclidean or Minkowskian metric.

yes. It does show up in gr. In gr, gamma (ratio of coordinate tmie to proper time) is a function of both speed and the gravitational potential (especially when g_0t =0).

Thanks. What is "g_0t"? Aren't zero and t as metric tensor subscripts used to mean the same thing?

Oops! You're right! Sorry about that. I meant to write g_0k = 0, k = 1,2,3. I can send you a PM which shows the calculation if you'd like? Its far too difficult for me to do that in PM since all I have to do is send you a URL (which we're not allowed to post in open forum).

That's wierd that you can't post URLs. I am always interested in reading new material related to GR, so I would make as much use of it as snoopies.

Correction: People are not allowed to post URLe to pages under their personal websites. The powers that be never made sense to me on this point so if you want to know the real reason you'd be better off asking a moderator why this is policy.